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A159299 Number of n-colorings of the 4 X 4 Sudoku graph. 2
0, 0, 0, 0, 288, 166560, 33539040, 2350746720, 75756999360, 1388552614848, 16744788486720, 146769785743680, 1002373493948640, 5606534724167520, 26640793339768608, 110556058012152480, 409297168707073920, 1374572399886053760, 4243833928227876480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The 4 X 4 Sudoku graph is a septic graph on 16 vertices and 56 edges. a(n) gives the number of 4 X 4 Sudoku solutions, if each of up to n numbers is allowed only once in every row, column and block.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: 10.1088/1367-2630/11/2/023001.

Eric Weisstein's World of Mathematics, Chromatic Polynomial

Wikipedia, Mathematics of Sudoku

Wikipedia, Sudoku

Wikipedia, Sudoku algorithms

Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

FORMULA

a(n) = n^16 -56*n^15 + ... (see Maple program).

G.f.: -96*x^4*(343316843*x^12 +4128584684*x^11 +20203233398*x^10 +50370257700*x^9 +68017469565*x^8 +50271571704*x^7 +20027437332*x^6 +4145554824*x^5 +419198325*x^4 +18781660*x^3 +320278*x^2 +1684*x +3)/ (x-1)^17. - Colin Barker, Aug 04 2012

EXAMPLE

For n=4 colors one of the 288 possible colorings is given by this Sudoku:

+---+---+

|1 2|3 4|

|4 3|2 1|

+---+---+

|3 1|4 2|

|2 4|1 3|

+---+---+ .

MAPLE

a:= n-> n^16 -56*n^15 +1492*n^14 -25072*n^13 +296918*n^12 -2621552*n^11 +17795572*n^10 -94352168*n^9 +392779169*n^8 -1279118840*n^7 +3217758336*n^6 -6107865464*n^5 +8413745644*n^4 -7877463064*n^3 +4436831332*n^2 -1117762248*n: seq(a(n), n=0..20);

CROSSREFS

Cf. A107739, A182866.

Sequence in context: A300052 A037946 A282102 * A008695 A047805 A173150

Adjacent sequences:  A159296 A159297 A159298 * A159300 A159301 A159302

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Apr 09 2009

STATUS

approved

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Last modified November 20 05:07 EST 2019. Contains 329323 sequences. (Running on oeis4.)